What does modestly mean?

To dress modestly means to dress conservatively.

Not flashy, for women not to be dressed to show-off their body or their appearance.

Modest, means not to be boastful or to have an over inflated idea of your own importance.

So in dress sense it means, not to show expensive trappings on your clothes like company logos or lavish trim. Do not expose bare flesh, in order to be provacative.